The canon Wiki provides is no doubt inerrant

however NFL Films already had dubbed Pittsburgh the "Team of the 70s" even though Dallas actually won more games in the 70s than even the Steelers, should you denounce this title? Anyhow the editor of the 1978 highlight reel wanted a snazzy title and noted that Cowboy fans were without fail across the country at every venue to see their beloved team. He chose the flattering mantle of "America's Team" without Art Rooney's permission, Tom Landry actually was intially opposed to this nickname because they were already the envy of the NFL and didn't want any more fodder to exist for opponents. He finally warmed to it however as the media took hold of it and ran with it.
Thus "America's Team" is forever synonymous with the Dallas Cowboys.